The nonlinearity in an optical fiber is originated from the Kerr effect, that is, the phase of transmitted light will be changed along with the variation of the power. Such nonlinearity is coupled with other linear effects (such as dispersion, and polarization mode dispersion, etc.), such that distortion occurs on the waveform of an optical signal at the receiver side.
It is found in studies that nonlinear Schrödinger equation may well describe the coupling between such two kinds of effects in the optical fiber. For the convenience of analysis, in a wavelength division multiplexing (WDM) optical communication system, the function of the nonlinearity may be deemed as two parts by some mathematical deformation: one part is originated from interactions between a plurality of channels (different wavelengths), and the other part is originated from interactions of the present channel (with the same compensation). In long-haul transmission, if the transmitted signal is a polarization multiplexed signal, a vector nonlinear Schrödinger equation may be substituted by a Manakov equation, in consideration of a statistical result of random birefringence in the optical fiber.
As the rise of transmission rate of single channel, the effect of intra-channel nonlinear originated from the present channel on the performance of a system becomes a problem drawing more and more attention of the people. When the rate of the single channel reaches 40-60 Gbits/s or more, the pulses within the same channel will be greatly widened and overlapped each other due to the effect of dispersion, and with the effect of the nonlinearity, energy exchange will occur between the overlapped pulses. In such a case, even though the residual dispersion in the link was compensated for at the receiving side, the system would still be severely nonlinearly damaged. The effect of nonlinearity within the channel on the system includes: timing jitter, signal amplitude fluctuation, and generation of ghost pulse.
For a long-haul optical communication system, how to compensate for or mitigate the cost of nonlinearity within a channel is an important question for study. Studies have been done with respect to design of link, DSP processing of receiver and coding of transmitting signal. A method for mitigating nonlinearity by subtracting nonlinear perturbation at a receiver side has been proposed in the prior art, refer to Reference [1] for details. Such a method is based on double oversampling, wherein a perturbation item is equal to a weighted sum of products of a series of three items (symbol information data of three moments), and the weighted value is decided by the dispersion, gain/attenuation and nonlinear coefficient of the link. The advantage of the method exists in the reduction of complexity, and especially in a PSK system, a pre-compensated waveform may completely be realized by means of addition and subtraction.
Since a nonlinear Schrödinger equation has no analytical solution under normal conditions, numerical simulation is often needed to obtain waveform distortion introduced by nonlinearity. Split-step Fourier method is a numerical simulation method that is most often used, which may infinitely approach a real solution when the step size is sufficiently small. However, the disadvantage of such a method is that it is too complex, and the simulation of a link configuration often needs several hours. And at the same time, it cannot give some physically visual explanations.
In Reference [2], Mecozzi et al. use a one-order perturbation model to mathematically transform a nonlinear Schrödinger equation. As the waveform distortion introduced by nonlinearity may be deemed as a weighted sum of a plurality of product items, each of the items is a product of transmission pulse amplitudes of three moments, and the coefficient is determined by the dispersion distribution of the link. Similar to that in a conventional nonlinear Schrödinger equation for numerical solution, Mecozzi et al. make nonlinear modeling within a channel to be a pure addition effect, and distinguish the effect of the link from the effect of the transmitted signal.
In Reference [3], Ernesto Ciaramella et al. make nonlinear modeling to be a pure multiplication effect, using also the one-order perturbation theory. In comparison with the addition model of Mecozzi et al., this model may tolerate greater input power (nonlinear) for some link configuration, and when the nonlinearity is relatively small, the results obtained by the two are identical.
In Reference [4], another model for nonlinear noise is a model based on mix of addition and multiplication proposed by Bononi et al., which is obtained by directly modifying an addition model, wherein the multiplication phase is a constant for different symbols.
However, in the implementation of the present invention, the inventors found the disadvantages of the prior art exist in: the case where both of the additive perturbation quantity and the multiplicative perturbation quantity are related to the current symbols and previous and subsequent symbols is not taken into consideration, and the accuracy of the signal estimation cannot be further improved.
Following documentations are listed for better understanding of the present invention and the prior art, which are incorporated herein by reference, as they are stated herein.    [Reference 1]: L. Dou, Z. Tao, L. Li, W. Yan, T. Tanimura, T. Hoshida, and J. C. Rasmussen, “A low complexity pre-distortion method for intra-channel nonlinearity,” in Proc. OFC/NFOEC2011 Conf., Los Angeles, U.S.A., March. 2011, paper OThF5.    [Reference 2]: IEEE PTL Vol. 12, No. 4, 2000, Antonio Mecozzi et. al.    [Reference 3]: IEEE PTL Vol. 17, 2005, pp 91, Ernesto Ciaramella et. al.    [Reference 4]: IEEE JLT, 2002, pp 1102, Bononi et. al.